Center Point Construction and the Computational Mind

I was looking at Mary Douglas’s checklist for ring forms and realized that each item on it had a plausible interpretation in the domain of computation. So that’s where I’m going in this post. But that’s not where I start. First I want to talk a little about computation, then another look at Tezuka’s Metropolis, and then the Douglas checklist.

What is Computation, Anyhow?

If, when you think about computers and computation, you mostly think about numbers and arithmetic, then you’re likely to be puzzled, if not horrified, at the idea that literature is somehow computational. Literature, after all, is not about numbers – though the pages and chapters of books may be numbered.

But then, computation isn’t necessarily about numbers either. It depends on how you think of it.

“625” and “six-hundred and twenty-five” are strings of characters and each represents the same number. The first string is of the sort used in arithmetic calculation while the second is not, though not for any inherent problem. It’s a simple matter of convenience; the string of numerals is more compact, and hence more convenient, than the string of words. Note, however, that when “625” is read aloud it might sound the same as “six-hundred and twenty-five”, though it might also be abbreviated to “six-twenty-five”.

When you learn arithmetic you learn the tables for addition, subtraction, multiplication, and division. These tables consist of basic propositions about numbers and how they behave under those four operations. You also learn a handful of simple rules to be used in applying those operations to multi-digit numbers. What you are learning – and practicing, hour upon hour – is symbol manipulation, but symbol manipulation of a very restricted kind.

Ordinary language use, after all, is also symbol manipulation. And, while there are restrictions, and lots of them, the proper manipulation of the symbols of ordinary language is open ended in a way the arithmetic calculation is not. Perhaps the most fundamental difference has to do with the set of symbols used to spell the names of the entities.

For both arithmetic and natural language is finite and quite small. For arithmetic the set consists of ten numerals (0 1 2 3 4 5 6 7 8 9), four operators (+ - * /), and an equals sign (=). The symbol set for any natural language is complicated by the fact that, for written languages, there may not be a one-to-one relationship between the symbol set for the written and spoken versions. There we would have to have separate discussions for alphabetic and non-alphabetic writing systems. And in either case, the spoken language has prosodic features that are not well represented in the written language.

Consider written English. We have the 24 letters of the alphabet and a handful of punctuation marks. That’s finite and small. However, letter combinations are used to form words, but the way they are combined to do so is completely arbitrary with respect to what the words mean and how they are used. That gives rise to what linguists call duality of patterning; the fact that language is patterned with respect to sound (phonetics and phonology) and with respect to meaning (semantics and syntax).

That isn’t the case with arithmetic. There is a systematic relationship between how a number is spelled and the value of the number designated by its name. Thus the spellings tell us that, of “478”, “829”, and “321”, 829 is the largest and 321 is the smallest. But the spellings of “dog”, “dot”, and “elephant” do not tell us which, if any, are living creatures. In particular, of the two that have similar spellings, one is living, the other is not. The third (“elephant”) is also a living creature though its spelling shares no letters with “dog”.

But the basic point still stands, both language use and arithmetic calculation are forms of symbol manipulation. Rather than continue on in this vein, I’ll refer you to a post where I say a bit more along these lines, Three Notes on Literature, Form, and Computation. I want to pursue a specific example before turning to Douglas’s ringform checklist.

A Simple Example: Keeping Track of Time

Let us consider one of our examples of center point construction, Osamu Tezuka’s Metropolis.

First of all there is basic convention about the relation between the flow of time in the story and the placement of actions and events in panels on the page. The Japanese read books with the spin facing to the right and they read individual pages right-to-left, top-to-bottom. In the English translation of Metropolis, the pages have been flopped so that one reads it in the order normal for English-language books. So, time flows from first-to-last between pages, and top-to-bottom, left-to-right on a single page.

This is simple stuff, and obvious enough. If I weren’t writing about computation, I wouldn’t even mention it. But, as I AM writing about computation, it’s useful to be reminded of these details. Computation, real computation, is a physical process and these are physical details of the reading process. And that, I am arguing, can usefully be thought of as a computational process.

So, we’re reading Metropolis. As we reach page 78 one of our protagonists, Detective Mustachio, is locked in an underground room that is being flooded with poisonous gas. The first panel at the top of the next page, 79, says “Two or three days later…”. The next panel shows a little girl standing on the sidewalk in front of a store and selling violets.

So, we have left one plot line and picked up a different one. This plot line continues through to the top of page 89; and we pick up a third plot line at the bottom of that page. That continues to page 94, where it merges back into the second plot line, which continues through to the bottom of page 98. Given the conventional relation between the passage of time in the story and the depiction of events on the page, we know that some amount of time has elapsed between page 75, right after we left Mustachio trapped underground, and our current place in the book (98). But the amount of time that elapsed is not at all clear. There are no dates, no calendars, no clocks, and no indications of any transition between day and night. Judging by the events, we’ve got several hours to a day, perhaps more; but it’s really difficult to judge.

Anyhow, what happens when get to page 99? You guessed it. The first panel on the page has a marker: “Meanwhile in the underground headquarters, something was about to happen…” And we rejoin Mustachio who is rescued by giant rats (who look very much like Mickey Mouse). About 10 pages later, on page 108, Mustachio joins the characters from the second plot line, the one we joined on page 79.

And THAT, that rejoining, is what aroused my suspicion that something interesting was going on here, something that might indicate center point construction. For we’ve also passed through the physical center of the book by the time we reach page 99.

That rejoining was ALSO and necessarily a jog backwards in time. But how, exactly, did I know that we went backward in time? The text doesn’t explicitly say that. All it says at the top of 99 is “Meanwhile…”, and, while that does imply that we may be going backward, the implication isn’t a strong one. (I don’t know what the Japanese says, but it doesn’t really matter for the matter I’m exploring, which is about texts in general, not about that particular text).

In any event, implication means that the reader has to do some thinking, not necessarily deep thinking, but thinking. The real clue, however is that note at the top of 79 – “Two or three days later…” – along with, and this is important, along with that convention about how story time is mapped onto page space in the text. If the convention were different, if there were no convention at all, then the fact that 20 pages had elapsed by the time we rejoined Mustachio might not have meant that all of a sudden we had to go back three or four days when we went from 98 to 99. We might have been going backward for all of those 20 pages.

What’s the point of all this? you may ask. Simple, when I talk about literary form as computational form, or about reading as a computational process, that’s the kind of thing I have in mind, that process whereby I was effortlessly able to infer that, zap!, I was moving back in time at the top of page 99. That’s a simple thing, but if you can’t do it, you’ll be lost.

I’ll have more to say about that example in the next section.

Details such as those are critical the proper functioning of a computational device, whether it is a digital device realized in silicon-based hardware or an analog-digital device realized in the organic materials of an animal or human brain (you do understand the distinction between digital and analogy, don’t you?). The exact nature of the details will depend on the nature of the device, but every device requires them. If you want to carve nature at its joints, you have to know where the joints are. Those details are indicators of where the joints are.

Douglas’s Checklist as Signs of Computation

Now let’s look at Douglas’s ring form checklist. I’m going to read it as a series of aids to the mind considered as a computational system. The features Douglas points out tell the mind things it needs to know in order to perform an effective computation.

What its computer, of course, is the meaning of the text. Just how it does that, of course, remains something of a mystery even after five or six decades of work specifically devoted to thinking about the mind as a computational device. But we don’t need to be able to solve the mystery in order to identify some of the clues that will contribute to the solution.

I need to say one or two more things before we look at the checklist. Computing is about resources, time and memory space. Each computational operation takes time. The more operations, the more time they require. The critical thing, though, is that the number of operations be finite. If they aren’t, then the computational will never end.

Memory space is physical too. If you own a thousand books, then your library needs shelf space for a thousand books. If the books are electronic, then your reading device, whether or special purpose book device or your computer, needs to have enough computer memory to store them.

We don’t really know what the memory capacity of the brain is, nor do we know how things are encoded. It may well be that for many purposes the capacity is unbounded. But there’s still a problem, organization. What’s the point of having enough space for your collection of 100,000 books if you don’t know how to find them? The mind’s the same way, and we forget things. If we search long enough, we can find things, but that time would be better used otherwise.

So, for the purposes of this discussion, memory capacity turns out to be a matter of time as well. Things have to be arranged so we can find them in time to get on with the story.

What I will do, then, is take the seven criteria Douglas proposed for ring forms (Thinking in Circles, pp. 36-37) and provid a brief computational gloss on each one of them. The glosses will necessarily be incomplete and open ended, as I don’t really know how the mind works. But I can at least indicate how the features Douglas picks out contribute to managing a computational process. I will indent her criteria, but not my gloss on it.

1. Exposition or Prologue: There is generally an introductory section that states the theme and introduces the main characters…

We have to initialize the computation. The theme indicates some of the nature of the coming computation, the resources we’ll need, as does the introduction of characters. We’ve got to be prepared to keep track of each character and so set aside memory space for each one. In effect, we set up a space in memory for each character and arrange things in a way appropriate for the computations required by the theme. Of course one has to do this with any narrative, whether or not it has a ring form. And expository openings are in fact quite common.

2. Split into two halves: If the end is going to join the beginning the composition will at some point need to make a turn toward the start…

While every narrative has a physical midpoint, this is something different. The notion that the computation is taking a “turn toward the start” at this point implies that the nature of the computation changes in some way. One regime has concluded and another one has begun. Just what these two regimes are, I can’t say because I don’t know how the mind works. I suspect, though, it’s something like this: once we’ve passed the midpoint, “everything is on the table.” Beyond that point we’re playing with the materials we’ve got. The nature of the computation changes.

Take Apocalypse Now. Once we’ve gone past the sampan massacre, the men in the boat are committed. Willard has killed for the first time in the film, and the others have killed for the first time ever. That won’t change. To be sure, we still have a way to go before Kurtz shows up, but we know he’s there. The photographer at Kurtz’s compound is a new character, of course, but he just elaborates on Kurtz himself. And the compound itself, the large buildings, that’s new too. But it’s window dressing.

3. Parallel sections: After the mid-turn the next challenge for the composer of a ring is to arrange the two sides in parallel…

I think parallel arrangement is similar to the split into two halves; it’s the same kind of thing, but of a very specific. Where this feature is missing we can talk of center point construction rather than ring form.

So, in Metropolis, Detective Mustachio gets backed into a locked room into which poisonous gas is introduced. That happens before the mid-turn. Once we’ve made the turn, we have to go back and either get him out of that room (in one kind of story) or kill him (in another kind of story). Ordinarily the introductory exposition or prologue will tell us what kind of completion to expect at this point.

4. Indicators to mark individual sections: Some method for making the consecutive units of structure is technically necessary…

That is, we’re breaking the overall computation into separate sub-computations. These indicators tell us when one computation has been completed or, alternatively, when the data (that is, text) for one computation is now complete and the computation can be run to conclusion.

In Metropolis, when you read “Two or three days later…” at the top of page 79, you know that one section has ended and another one has started. You put the Mustachio plot line on hold, so you can come back to it later, and prepare to meet a different set of characters doing different things in a different setting. The “Meanwhile…” at the top of page 99 serves a similar function.

5. Central loading: The turning point of the ring is equivalent to the middle term, C, in the middle term of a chiasmus, AB / C/ BA. Consequently, much of the rest of the structure depends on a well-marked turning point that should be unmistakable…

The central section in Metropolis is well marked. It begins on the top half of page 84, which is a single panel, which makes it an unusually large one. Further, it doesn’t have a border, the only panel in the entire text without one – well, not quite. There are some others, but they’re smaller and not so noticeable. In the lower part of the panel we have a mid-chest shot of Kenichi holding a book – the one telling the story of Michi’s origins and operation – and nothing else. There is no background. The upper half of the panel consists of a cloud of prose in which we learn the secrets of Michi’s manufacture. This section runs to page 94 and contains a number of large panels, some a half page or larger, and there’s page (93) consisting of a single large panel or three men in conversation. The three thought/speech balloons on the page are so large that they move beyond the panel boundary, the only place in the text where that happens. Which is to say that, independently of what actually happens in this middle section (84-94) it has these formal features that mark it as different from any other sequence in the text.

So, the center point sequence is well marked, we know when it begins and when it ends, and the information it gives us “gets all the cards on the table.” In Metropolis we know that Michi is bi-gendered, something we hadn’t known before, and that his/her life depends on synthetic cells. We learn about Michi’s super powers and we also learn that strange things are happening to life forms all over the world.

6. Rings within rings: As Otterbo pointed out, the major ring may be internally structured by little rings…

In effect, a ring is a particular way for structuring a narrative into different components. One, some, or any of those components can itself be a ring. Presumably, however, we are not going to allow rings to be embedded within one another very deeply. Again, any narrative can be composed of subnarratives, and perhaps of any formal type. I’m not aware of any such features in Metropolis, but I’ve not checked for them either.

7. Closure at two levels: By joining up with the beginning, the ending unequivocally signals completion. It is recognizably a fulfillment of the initial promise…

Computationally this is simple: the computation is ended and a result has been obtained. These are two different things. The computation might end because the machine is turned off, or it might end because any computation that runs on too long is simply stopped, like chess games where no pieces are exchanged in a long series of moves. No one wins the game, but it’s over.

At this point I suppose it would be useful to tell you a bit more about Metropolis than I have so far. When Mustachio and Kenichi find Michi, he/she is bereft. The man who created Michi, Dr. Lawton, is dead and Michi goes on a quest to find his/her true father and find out whether or not he/she is human. We of course know the answers to those questions and so know that Michi’s quest is doomed. When Michi dies at the end, that fate is fulfilled. At the same time, Michi’s classmates come to the hospital room to bid Michi farewell, which is a different kind of fulfillment.

Form and Computation

Though Douglas used a computer in her work – we corresponded through email and exchanged text files – she didn’t have any particular knowledge of or interest in computing. Yet, when it came time to create rules of thumb for identifying ring form texts, the rules she came up with have a computational feel to them.

Why? Perhaps it’s because that’s just how language, the mind, and texts work. What else is there?

I am aware that THAT’s not an argument. It’s an assertion. But it’s not an empty one. The mind may not be a digital computer – it surely isn’t – but it faces similar problems and so arrives at similar solutions.